Game Theory: An Overview of Everything You Need to Know

What is Game Theory?

Game theory is a branch of mathematics that analyses optimal decision-making in strategic settings.

It deals with situations involving cooperation and conflict between rational and self-interested players.

Game theory has applications in psychology, economics, social interactions, computer science, business, negotiation, war, politics, biology, sports and games of all kinds.

Traits of games

Games can come along with many traits. This list is not exhaustive but has many of the practical ones.

Finite Games & Infinite Games.

They have different characteristics and approaches to take when trying to optimize results.

Characteristics of Finite Games:

• Played for the purpose of winning

• Defined players

• Fixed rules

• Clear end-point

Examples include poker, chess, sports, and finance.

Characteristics of Infinite Games:

• Played for the purpose of continuing to play

• Known & unknown players

• No agreed upon rules

• No end-point

Examples include fitness, business, politics, and marriage.

Sequential or Simultaneous

Sequential games are games in which players take turns choosing their actions. Chess is a great example. In this type of game, the previous decision of the opposing player informs each current decision.

Simultaneous games are distinctly different from sequential as both players make their decisions at the same time. The decision is only based on speculation of what the opposing player will do. Typically, the chosen strategy does not change based on the opponent. Rock paper scissors is an example of a simultaneous game.

One-off or Repeated (Iterated)

One-off games get played only one time. The best strategy for this type of game is typically selfish and to defect against the opposing player.

Repeated games are different as the same game with the same players gets repeated several times. The best strategy is generally to be nice, retaliatory, and forgiving. A Tit-for-Tat strategy is a good choice for repeated games with no known end: each time they defect you retaliate with defection.

Cooperative or Non-Cooperative

Cooperative games often allow players to communicate, negotiate, and form 'coalitions'. Cooperation is initiated and sustained because it maximizes their joint payoff.

Non-cooperative games happen when the players can't or won't coordinate their actions. They act independently and rationally, considering the expected responses of other players.

Symmetric or Asymmetric

Symmetric games offer the same optimal strategy to each player. Even with an interchanging opponent the players will choose the strategy.

In Asymmetric games, the strategy that offers benefits to one player may not be as beneficial to another. The players adopt different strategies. The decision-making depends on the strategies and decisions of other players.

Outcome of games

Zero Sum or Non-Zero Sum

Zero sum games are characterized by the loss of one player being transactionally gained by another. It's named this way because the net losses and gains are equal to zero. Business competition is an example of this, especially in the tech industry: when somebody buys an Apple iPhone they won't get an Android phone too. Zero sum games are ruthless because they have winner takes all dynamics (like poker).

Non-Zero sum games are characterized by the net loss or gain being more or less than zero. An example of this is oligopolies where collaboration can expand the size of the market, or the lack of it can diminish the market affecting both parties.

Positive Sum or Negative Sum

Positive and negative sum games are the two types of non-zero sum games.

Positive sum games have a net benefit to the system and players. Capitalism is positive sum because when somebody buys a car the company and employees now have more disposable income and the buyer a car. All the capital that exists in the world today was created. Capitalism does have flaws, but the net benefit to the system is positive. Positive sum games can have win-win situation dynamics.

Negative sum games have a net loss to the system induced by the parties involved or an outside force. Pirates stealing from a cargo ship is an example of this because the net losses are higher than the pirate's payoff. Typically, war is a negative sum game, both parties suffer a net loss of value (soldiers, civilians, supplies, loss of infrastructure).

Important games to understand

Prisoner's Dilemma

In the Prisoner's Dilemma, two suspects are given the option to either cooperate or betray, staying silent or confessing. The dilemma is as follows:

• If both cooperate: Both get 1 year (total payoff: 2 years).

• If one betrays: Betrayer gets 0 years, cooperator gets 10 years (total payoff: 10 years).

• If both betray: Both get 5 years (total payoff: 10 years).

The optimal outcome is for both to cooperate, but there is temptation to betray for personal gain which often leads to suboptimal results.

Stag Hunt

In the Stag Hunt, two hunters can jointly hunt a stag or individually hunt a rabbit. Hunting the stag requires cooperation and results in a larger payoff, but if either hunt the stag alone the chance of success is minimal.

Volunteer's Dilemma

In the Volunteer's Dilemma, a mutually beneficial outcome for the group will result from one player doing a task while the others benefit without doing anything. Meaning each player has to decide whether to be the one to step forward or not. Since there is no added benefit for the volunteer, there is no incentive for acting since everyone else benefits as well.

Bayesian Games and Beliefs

Bayesian Games are characterized by having incomplete information. Concepts such as private knowledge are introduced. Players have beliefs (characteristics or information) about the other players. Strategies are based on the beliefs of the player. Bayesian games include a set of possible 'types' (beliefs) for each player and a probability distribution over these types.

Strategies

Pure and Mixed

Pure strategies are an unconditional decision adopted by the player in a situation. The player abides by their pure strategy regardless of anything that happens in the game. In Rock Paper Scissors an example of a pure strategy would be only playing rock.

Mixed strategies are when the strategy chosen out of all the available options is decided on based on a probability distribution. A player uses a mixed strategy only when they are indifferent to a set of pure strategies, and when the opponent can benefit from knowing the next move. An example of a baseball pitcher adopting a mixed strategy is alternating between knuckleballs, fastballs, and curveballs.

Dominant and Dominated

Dominant strategies happen when a pure strategy will always yield the best payoff regardless of the opposing player's decision.

Dominated strategies are decisions that will always lead to payoffs less than a different strategy the player could choose. There are both strongly and weakly dominated strategies. Always rule out strongly dominated strategies. Weakly dominated strategies can remain viable options in the decision-making process.

Minimax and Maximin

Minimax strategies aim at minimizing potential losses. The player considers the opposing player's strategy which would result in the most personal loss and selects the best response. This strategy ensures the losses sustained are as minimal as possible.

Maximin strategies aim at maximizing the minimum payoffs. The player considers the worst outcome for each strategy and picks the one with the best minimum payoff. This strategy ensures that even in unfavourable scenarios the player secures their best option.

Nash Equilibrium

A Nash Equilibrium is a situation where both players are using their optimal strategy. The state gives no incentive to any individual player to change their strategy because they both get the optimal payoff. No benefit is gained by changing strategies assuming the other player's strategy remains the same. A game can have several Nash Equilibria or none at all.

Applicable fields

This is by no means an extensive list, but it gives insight into a few areas of application. Notable fields not included are politics, computer science, war, and sports.

Business

In business, Game Theory is a powerful analysis tool that aids the decision-making process. It can be used to analyze competitive environments such as oligopolies, optimize pricing strategy based on the likely market and competitor response, help anticipate the competitor's moves, and improve upside and risk management. Game theory can inform business negotiations, and show opportunities of cooperation for the gain of both parties.

Economics

Game Theory revolutionized the field of economics and is the direct cause of many recent advancements. Using game theory in economics, researchers can study behaviours like price-fixing, collusion, market competition, and strategic decision-making by firms. This analytical tool aids in understanding how players' choices impact each other's payoffs and how strategic interactions influence market dynamics, pricing strategies, and overall economic outcomes

Biology

Biology applies Game Theory to understand the evolution of behaviours and strategies among organisms. It provides a framework for analyzing how individuals interact in their environments and with each other, focusing on the costs and benefits of these interactions. In evolutionary game theory, treating strategies as phenotypes helps to explain why certain behaviours like cooperation, conflict, and altruism evolve and become stable within certain populations. The outcome of interactions is based on a payoff matrix that compares the relative costs to the benefits obtained, ultimately influencing an organism's fitness and reproductive success

Practical use

Negotiation

Negotiation is a much bigger part of our daily lives than many realize. Deciding what movie to watch, which restaurant to eat at, or who takes the garbage out is all negotiation. Negotiation is often a positive sum game and is often beneficial to both parties, the total pie gets enlarged making both sides better off. It's quite rare that negotiation is zero sum. A minimax strategy is a good choice for negotiating, minimizing your opponent's maximum payout is usually a good strategy. Making the first offer is advisable as you're able to frame the negotiation to your advantage. Reciprocity (tit-for-tat) is an optimal trait for negotiation as you can expect to get what you give. Thinking of negotiations through the lens of Game Theory can help determine if someone has a dominant strategy, find win-win situations, and to choose the optimal strategy based on the opponent's likely decision. Remember that trust and reputation is the foundation of negotiation and it is the better choice to incur cost rather than lose face.

Avoid Negative and Zero Sum Games, Play in Positive Sum Games

Try to find situations where collaboration increases the total value (positive sum games), rather than engaging in conflicts where one's gain is another's loss (zero sum games). If you play in win-win situations you will get more payoff, and make fewer enemies. Some zero-sum games are unavoidable (such as status). Aim to spend most of your energy in positive sum games. Avoid negative sum games where the interaction costs more than the benefits gained, leading to a net loss for all parties involved.

Pareto Optimality

Pareto optimal outcomes are where resource allocation cannot be improved for one individual without harming another. Aim for solutions which maximize overall benefit without causing harm to others. Pareto optimality ensures efficient allocation of resources.

Tit-for-Tat Strategy

The Tit-For-Tat strategy is an effective approach to certain repeated games. Start with cooperation and replicate your opponent's previous action, rewarding cooperation and punishing defection, fostering mutual cooperation. This strategy promotes a stable, reciprocal relationship and can deter exploitative behaviour in ongoing interactions. The strategy can be distilled into 3 main traits: Nice (cooperate), retaliatory (punish defection), and forgiving.

Everyday Life

In strategic situations and decision-making you can apply Game Theory to understand the strategic interactions involved. For instance, when choosing a movie to watch with friends one could use game theory to predict the preferences of others and suggest a movie that maximizes overall satisfaction. In more significant instances such as career or investment decisions one could use game theory to evaluate the potential actions and reactions of employers or market decisions, leading to more informed and strategic choices.